By default, HOME is set to / in /etc/crontab.
Without a HOME line in user crontabs, HOME is the home directory in /etc/passwd of the crontab owner.

This caused me problems when I tried to execute a MySQL backup script via run-parts that depended on ~/.my.cnf in the user's home directory. As a workaround, I modified the script to set the HOME environment variable rather than make a global change in /etc/crontab for all run-parts scripts.